Assuming you mean late August - early September, the weather should be as Sinister Angel said - highs in the 70s with some days in the 80s. You can still have some 90 degree days, but not likely. With autumn approaching, there may be some days with highs in the 60s. Overnight lows are usually in the 60s with some nights in the 50s. It's usually not very rainy then and you won't get any snow. Trees won't be turning yet.
What kind of outdoor relaxing do you like? Once schools start (usually right after Labor Day which is Sep 1 this year) the beaches and parks are very empty during the week. Bay City is on Saginaw Bay which connects to Lake Huron. Aside from the lake & bay, you can go north and find some great rivers to canoe. Here is the state tourism site:
http://www.michigan.org/
Other places to visit:
- Frankenmuth is a kitchy Bavarian-style town, but has Bronner's which is the world's largest Christmas shop.
- Detroit has some excellent museums and concerts. They also have Tigers baseball and Lions football. Those don't look to be too excellent this year.
- Dearborn (near Detroit) has the Henry Ford Museum and Greenfield Village which are great day-long destinations.
- Dundee (on US-23 heading toward Ohio) has Cabela's which is huge hunting, fishing, and camping equipment store. It's supposedly the top tourist destination in the state.
Michigan Weather 
